Experience has shown me that if it's not assessed, it's not valued. Here's what I value:
Rigorous and challenging mathematics
An appreciation of the connections within mathematics
A willingness to investigate mathematical ideas
An understanding that practice is necessary for success in mathematics
Successful study habits- consistent practice, preparedness, etc.
Academic Honesty
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Grading
This is the grading system that I've implemented to support the above philosophy:
Responsibility (10%)
Students start each quarter with 20 responsibility points (about one per day). If they come to class without their homework attempted (something written for each problem), they lose a point. At the start of the year, the homework check is often done by asking students to copy down their working for three homework problems (from their notebooks, without their text or homework sheet)- this allows me to emphasize that something needs to be written for every problem. A responsibility point can also be lost for coming to class unprepared- no text, pencil, notebook, etc. Turning in a required assignment late also results in a lost responsibility point. Using your computer irresponsibly (listening to music, surfing the internet, doing email, checking facebook, etc) during class also results in a lost responsibility point.
There's really no reason to lose a responsibility point, and students regularly keep all 20 points.
During quizzes and tests, homework will be collected. A few problems will be randomly selected to be checked. I will be looking to see that the problem has been completed and that the problem has been corrected if necessary
Quizzes(30%)
Each unit includes one or two quizzes which are merely homework problems with a number or two changed. Wordings of problems are unchanged. I write quizzes by choosing 7 or 8 homework problems from any assignment up to the previous night's (to allow students to ask questions on the new assignment). Students with limited time for revision know exactly what to expect on a quiz. In this way, students who keep up with homework assignments and make sure they can do each problem are rewarded while those who are working from the provided homework answers or who receive excess help from friends are penalized.
Tests (50%)
Tests generally last all period. They are usually between 9 and 13 questions long. Students may use calculators on the first page. When they are ready to give up their calculators, they receive the second page and they may then work on both pages for the remainder of the period. The questions assess the content and skills of the unit, and thus will usually not be identical to previous questions asked in class or on homework. In lower level classes, a question may consist of several parts which may connect or may be a set of one step exercises on a concept. There will usually be at least one question which requires some explanation. Questions will be of varying difficulty levels; it is rare for a student to get all questions completely correct. These tests are "finely crafted opportunity days" (opportunities to show me what they've learned over the unit!), and they generally take a while to write.
When students finish the timed portion of the test, I quickly mark each question either right or wrong. To be marked right, the question must be answered completely correctly. I then scan a copy of each student's test on the photocopier to keep a record of the work done in class. Students usually collect their tests by the end of the day and begin work on the next portion- Supercorrections.
Supercorrections are where students go back and correct their tests and then reflect on each problem that they missed. They may receive any assistance they'd like- from fellow students, me, parents, websites, etc. They write a correct solution for the problem missed and then write a reflection on the problem- what concept they were missing, what silly mistake they made, etc. To make a correction super, I encourage them to do something extra- show alternate methods of solution, connect to a different problem, etc.
Here are the instructions, rubric and forms for Supercorrections (these files provide the details for how Supercorrections work).
I usually devote one class of homework (the day of the test) and some class time to Supercorrections. Supercorrections are due a week or so after the timed portion of the test to allow students to come in for extra help if they need it.
Here are several examples of recent Supercorrections received (you may want to print the PDF files or zoom in to read them more clearly):
The student who didn't revise for the test and whose work during the unit was spotty at best (here). He used the Supercorrections to finally learn the basics of logarithms. The rubric means that his test score is still low- he can't afford to do this every unit- but hopefully he realizes that he can do better with consistent effort.
The student who works hard but finds the tests challenging (here and here). This student is rewarded for hard work and her ability to handle challenging problems improves through her effort on Supercorrections. This type of student is often surprised that problems that seemed quite difficult at first are actually not that hard.
The strong mathematics student (here). This student can still learn from challenging tests and reflections on Supercorrections.
Supercorrections place emphasis on working accurately in a timed situation (full marks are only possible by getting a problem correct the first time). Students learn to check their work carefully so that they don't need to write a Supercorrection for a careless mistake. More importantly, though, they provide time and space for reflection and more reasoned analysis. It also allows me to make summative unit test into a formative learning opportunity.
Academic Honesty There is an old saying that “Honesty is the best policy.” This goes beyond the classroom. Here is an essay from Real Simple magazine on the cumulative effects of lies (even white lies) in your daily life. In the classroom, lying has a special name: cheating. · Copying someone else’s homework is cheating. · Letting someone copy your work is cheating. · Looking at someone’s work during a quiz or test is cheating. · Asking another student about a test or quiz that you haven’t taken yet is also cheating. · Telling another student about a quiz or test they haven’t taken yet is cheating. I can accept a student saying that “I just couldn’t get it done” much easier than seeing a paper that is the work of another person. Please do not put yourself, a friend or me in a situation that none of us will be comfortable with. When it comes to academic honesty, take responsibility for your own education and if in doubt, ask!
Two tips for avoiding cheating on homework:
1) Never give your homework notebook to another student. The moment you do, you lose control of the situation, and if that student copies your work, YOU are still responsible – you have cheated.
2) If you do look at someone else’s solution to a problem, put away that solution before attempting it yourself – this way the solution will be in your own words.
Cite your sources:
On a project, supercorrections, or homework, take the two seconds necessary to cite your sources(friends, tutors, other teachers, books, internet) . It keeps you honest and it honors the ideas of others. In that spirit, I would like to take the opportunity to thank my friend and former colleague, William O’Brien, for graciously allowing me to use his words and ideas in this document.
The Sandy Puckett* Memorial IOU (extra credit)
I have a box of extra credit IOU cards. Each one is worth 0.1 points added to any quarter grade. Students earn IOUs by making clever observations in class, finding errors in my board work, winning warm-up or revision games, doing problems from the NCTM Mathematics Teacher calendar, or working on some other extra credit problem (which usually arise from a class discussion).
I don't keep a record of IOUs awarded; students must keep their own IOUs. At the end of the quarter, I give students their grades to the nearest tenth. If they choose to use some IOUs to raise their grade, they do so then by giving me the required number of IOUs at that time. *This idea came from Sandy Puckett, an inspirational teacher and artist who passed away on 3/14/2009 (Pi day!). His sketches adorn the IOU.
Final Exam: aka Final Opportunity Day
The final exam has no Supercorrections. It is the students' final opportunity to show me what they know- a true summative assessment. ----
Use of class time
I find that this system of grading frees my use of class time. Since homework is not collected until the end of the unit, I may use an assignment to introduce a topic, knowing that we will go over it before students need to submit their final work. I give homework every class, and I always give time for questions from all homework assignments, but this is about the only constant. Some lessons are more investigative; others are more teacher centered.
I also find that responsibility for learning shifts from the teacher to the students in this system. Our class time together is a chance for students to ask questions and work on their ongoing homework assignments, and it is also a safe setting for investigating the challenging questions that will eventually be asked on the end of unit tests.
Philosophy
Experience has shown me that if it's not assessed, it's not valued. Here's what I value:
----
Grading
This is the grading system that I've implemented to support the above philosophy:
Responsibility (10%)
Students start each quarter with 20 responsibility points (about one per day). If they come to class without their homework attempted (something written for each problem), they lose a point. At the start of the year, the homework check is often done by asking students to copy down their working for three homework problems (from their notebooks, without their text or homework sheet)- this allows me to emphasize that something needs to be written for every problem. A responsibility point can also be lost for coming to class unprepared- no text, pencil, notebook, etc. Turning in a required assignment late also results in a lost responsibility point.Using your computer irresponsibly (listening to music, surfing the internet, doing email, checking facebook, etc) during class also results in a lost responsibility point.
There's really no reason to lose a responsibility point, and students regularly keep all 20 points.
Homework (10%)
During quizzes and tests, homework will be collected. A few problems will be randomly selected to be checked. I will be looking to see that the problem has been completed and that the problem has been corrected if necessaryQuizzes(30%)
Each unit includes one or two quizzes which are merely homework problems with a number or two changed. Wordings of problems are unchanged. I write quizzes by choosing 7 or 8 homework problems from any assignment up to the previous night's (to allow students to ask questions on the new assignment). Students with limited time for revision know exactly what to expect on a quiz. In this way, students who keep up with homework assignments and make sure they can do each problem are rewarded while those who are working from the provided homework answers or who receive excess help from friends are penalized.Tests (50%)
Tests generally last all period. They are usually between 9 and 13 questions long. Students may use calculators on the first page. When they are ready to give up their calculators, they receive the second page and they may then work on both pages for the remainder of the period. The questions assess the content and skills of the unit, and thus will usually not be identical to previous questions asked in class or on homework. In lower level classes, a question may consist of several parts which may connect or may be a set of one step exercises on a concept. There will usually be at least one question which requires some explanation. Questions will be of varying difficulty levels; it is rare for a student to get all questions completely correct. These tests are "finely crafted opportunity days" (opportunities to show me what they've learned over the unit!), and they generally take a while to write.When students finish the timed portion of the test, I quickly mark each question either right or wrong. To be marked right, the question must be answered completely correctly. I then scan a copy of each student's test on the photocopier to keep a record of the work done in class. Students usually collect their tests by the end of the day and begin work on the next portion- Supercorrections.
Supercorrections are where students go back and correct their tests and then reflect on each problem that they missed. They may receive any assistance they'd like- from fellow students, me, parents, websites, etc. They write a correct solution for the problem missed and then write a reflection on the problem- what concept they were missing, what silly mistake they made, etc. To make a correction super, I encourage them to do something extra- show alternate methods of solution, connect to a different problem, etc.
I usually devote one class of homework (the day of the test) and some class time to Supercorrections. Supercorrections are due a week or so after the timed portion of the test to allow students to come in for extra help if they need it.
Here are several examples of recent Supercorrections received (you may want to print the PDF files or zoom in to read them more clearly):
Supercorrections place emphasis on working accurately in a timed situation (full marks are only possible by getting a problem correct the first time). Students learn to check their work carefully so that they don't need to write a Supercorrection for a careless mistake. More importantly, though, they provide time and space for reflection and more reasoned analysis. It also allows me to make summative unit test into a formative learning opportunity.
Academic Honesty
There is an old saying that “Honesty is the best policy.” This goes beyond the classroom. Here is an essay from Real Simple magazine on the cumulative effects of lies (even white lies) in your daily life. In the classroom, lying has a special name: cheating.
· Copying someone else’s homework is cheating.
· Letting someone copy your work is cheating.
· Looking at someone’s work during a quiz or test is cheating.
· Asking another student about a test or quiz that you haven’t taken yet is also cheating.
· Telling another student about a quiz or test they haven’t taken yet is cheating.
I can accept a student saying that “I just couldn’t get it done” much easier than seeing a paper that is the work of another person. Please do not put yourself, a friend or me in a situation that none of us will be comfortable with. When it comes to academic honesty, take responsibility for your own education and if in doubt, ask!
Two tips for avoiding cheating on homework:
1) Never give your homework notebook to another student. The moment you do, you lose control of the situation, and if that student copies your work, YOU are still responsible – you have cheated.
2) If you do look at someone else’s solution to a problem, put away that solution before attempting it yourself – this way the solution will be in your own words.
Cite your sources:
On a project, supercorrections, or homework, take the two seconds necessary to cite your sources(friends, tutors, other teachers, books, internet) . It keeps you honest and it honors the ideas of others. In that spirit, I would like to take the opportunity to thank my friend and former colleague, William O’Brien, for graciously allowing me to use his words and ideas in this document.
The Sandy Puckett* Memorial IOU (extra credit)
I have a box of extra credit IOU cards. Each one is worth 0.1 points added to any quarter grade. Students earn IOUs by making clever observations in class, finding errors in my board work, winning warm-up or revision games, doing problems from the NCTM Mathematics Teacher calendar, or working on some other extra credit problem (which usually arise from a class discussion).I don't keep a record of IOUs awarded; students must keep their own IOUs. At the end of the quarter, I give students their grades to the nearest tenth. If they choose to use some IOUs to raise their grade, they do so then by giving me the required number of IOUs at that time.
*This idea came from Sandy Puckett, an inspirational teacher and artist who passed away on 3/14/2009 (Pi day!). His sketches adorn the IOU.
Final Exam: aka Final Opportunity Day
The final exam has no Supercorrections. It is the students' final opportunity to show me what they know- a true summative assessment.----
Use of class time
I find that this system of grading frees my use of class time. Since homework is not collected until the end of the unit, I may use an assignment to introduce a topic, knowing that we will go over it before students need to submit their final work. I give homework every class, and I always give time for questions from all homework assignments, but this is about the only constant. Some lessons are more investigative; others are more teacher centered.
I also find that responsibility for learning shifts from the teacher to the students in this system. Our class time together is a chance for students to ask questions and work on their ongoing homework assignments, and it is also a safe setting for investigating the challenging questions that will eventually be asked on the end of unit tests.